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# Q.2 Solve the following: (a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score? (b) In an isosceles triangle, the base angle are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°?) (c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

(a) Let the lowest score be x.
Therefore Highest marks obtained = 2x + 7
According to question,
2x+7 = 87
= 2x = 87 - 7
= x = 80 /2
= x= 40
The lowest score = x= 40
(b) Let each base angle be x degrees.
Therefore Sum of all angles of the triangle (x + x + 40°) degrees.
We know that sum of all angle of a triangle is 180°
So, (x+x+40°) = 180°
= 2x +40° = 180°
= 2x = 180° - 40°
= x = 140° / 2 = 70°
Hence the base angle = x = 70 °
(c)Let the runs scored by Rahul = x
Runs scored by Sachin = 2x
According to question,
x+2x + 2 = 200
= 3x = 200 -2
= x = 198 / 3
= x = 66
runs scored by Rahul = x = 66
Runs scored by Sachin = 2x = 2×66 = 132